What Is a Rational Number? - mrscote

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To multiply 2 rational numbers, use the properties for determining the sign of the product of
2 integers to predict the sign of the product of the rational numbers. Then:
➤ If the rational numbers are in fraction form:
Use the procedures for multiplying 2 fractions to determine the numerical value
of the product.
➤ If the rational numbers are in decimal form:
Use the procedures for multiplying 2 decimals to determine the numerical value
of the product.
For example,
• When two rational numbers have the same sign, their product is positive.
a3 3
3 1 3
a 1 and
2 b 5 b 10
2 5 10
(1.5) (1.8) 2.7 and 1.5 1.8 2.7
• When two rational numbers have opposite signs, their product is negative.
3
3
1 3
a 1 and a 3
2 5 b 10
2 b 5 10
(1.5) 1.8 2.7 and 1.5 (1.8) 2.7
When we use brackets to write a product statement, we do not need the
multiplication sign. For the rational numbers above, we can write
3
2
a1 as a3 , and (1.5) 1.8 as (1.5)(1.8).
5 b 2 ba1 5 b
Example 1
Multiplying Rational Numbers in Fraction or Mixed Number Form
Determine each product.
a) a11 a21
b)
7 b 44 b
A Solution
a)
a22 a1 3 3 b 4 b
a11 a 21
7 b 44 b
Predict the sign of the product: since the fractions have the same sign,
their product is positive.
124 UNIT 3: Rational Numbers